Tìm x, biết:a)\(\left( {0,5.x - \frac{3}{7}} \righ...

A

- Hướng dẫn giải

Phương pháp giải:

Câu a: áp dụng kiến thức về tìm thành phần chưa biết trong phép tính.

Câu b: chú ý \(\left| x \right| = a > 0 \Rightarrow x =  \pm a\).

Câu c: chú ý \({x^2} = {a^2} > 0 \Rightarrow x =  \pm a\).

Giải chi tiết:

\(\left( {0,5x - \frac{3}{7}} \right):\frac{1}{2} = 1\frac{1}{7}\)

\(0,5x - \frac{3}{7} = \frac{8}{7}.\frac{1}{2}\)

\(\begin{array}{l}0,5x - \frac{3}{7} = \frac{4}{7}\\0,5x = \frac{4}{7} + \frac{3}{7}\\0,5x = 1\\x = 1:0,5\\x = 2\end{array}\)

\(\begin{array}{l}b)\left| {2 - 3x} \right| - 5 =  - 1\\\left| {2 - 3x} \right| =  - 1 + 5\\\left| {2 - 3x} \right| = 4\end{array}\)\(\begin{array}{*{20}{c}}\begin{array}{l}TH1:2 - 3x = 4\\3x = 2 - 4\\3x =  - 2\\x =  - \frac{2}{3}\end{array}&\begin{array}{l}TH2:2 - 3x =  - 4\\3x = 2 - \left( { - 4} \right)\\3x = 6\\x = 6:3\\x = 2\end{array}\end{array}\)

Vậy \(x \in \left\{ { - \frac{2}{3};2} \right\}\).

\(\begin{array}{l}c){\left( {\frac{1}{5} - \frac{3}{2}x} \right)^2} = \frac{9}{4} = {\left( {\frac{3}{2}} \right)^2}\\\begin{array}{*{20}{c}}\begin{array}{l}TH1:\frac{1}{5} - \frac{3}{2}x = \frac{3}{2}\\\frac{3}{2}x = \frac{1}{5} - \frac{3}{2}\\\frac{3}{2}x =  - \frac{{13}}{{10}}\\x =  - \frac{{13}}{{10}}:\frac{3}{2}\\x =  - \frac{{13}}{{15}}\end{array}&\begin{array}{l}TH2:\frac{1}{5} - \frac{3}{2}x =  - \frac{3}{2}\\\frac{3}{2}x = \frac{1}{5} - \left( { - \frac{3}{2}} \right)\\\frac{3}{2}x = \frac{{17}}{{10}}\\x = \frac{{17}}{{10}}:\frac{3}{2}\\x = \frac{{17}}{{15}}\end{array}\end{array}\end{array}\)

Vậy \(x \in \left\{ { - \frac{{13}}{{15}};\frac{{17}}{{15}}} \right\}\)

Đáp án: A.